Recent questions tagged sec-b

Find the integrals of the functions\[\cos2x\;\cos4x\;\cos6x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^3(2x+1)\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\sin x\;\sin2x\;\sin3x$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\sin^4x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\cos^42x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\frac{\cos2x-\cos2\alpha}{\cos x-\cos\alpha}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\frac{\cos x-\sin x}{1+\sin2x}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions\[\tan^32x\sec2x\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\tan^4x$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the function $\frac{1}{\sin x\cos^3x}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{\cos2x}{(\cos x+\sin x)^2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\sin^{-1}(\cos x)$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find the integrals of the functions $\frac{1}{\cos(x-a)\cos(x-b)}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x-1}{\sqrt{x^2-1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{4x+1}{\sqrt{2x^2+x-3}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{x^2-1}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{5x-2}{1+2x+3x^2}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{6x+7}{\sqrt{(x-5)(x-4)}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{4x-x^2}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+2}{\sqrt{x^2+2x+3}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{x+3}{x^2-2x-5}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the functions\[\frac{5x+3}{\sqrt{x^2+4x+10}}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions\[\frac{x}{(x+1)(x+2)}\]

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{2x}{x^2+3x+2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions$\;\large\frac{3x-1}{(x+2)^2}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{1}{x^4-1}$

asked Dec 5, 2012 by sreemathi.v

1 answer

Find a unit vector perpendicular to each of the vector $ \overrightarrow a + \overrightarrow b$ and $ \overrightarrow a - \overrightarrow b$, where $ \overrightarrow a = 3\hat i + 2\hat j + 2\hat k$ and $ \overrightarrow b = \hat i + 2\hat j - 2\hat k$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If a unit vector $\overrightarrow a$ makes angles $ \frac{\large \pi}{\large 3} $ with $ \hat i, \frac{\large \pi}{\large 3} $ with $ \hat j$ and an acute angle $θ$ with $ \hat k$ , then find $ θ $ and hence, the components of $ \overrightarrow a $ .

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that $ ( \overrightarrow a - \overrightarrow b) \times ( \overrightarrow a + \overrightarrow b) = 2 ( \overrightarrow a \times \overrightarrow b) $

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find $λ$ and $μ$ if $ ( 2\hat i + 6\hat j + 27\hat k)\times (\hat i + λ\hat j + μ\hat k) = \overrightarrow 0$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let the vectors $ \overrightarrow a, \overrightarrow b, \overrightarrow c$ be given as $a_1\hat i + a_2\hat j + a_3\hat k, \: b_1\hat i + b_2\hat j + b_3\hat k, \: c_1\hat i + c_2\hat j + c_3\hat k $. Then show that $ \overrightarrow a × (\overrightarrow b + \overrightarrow c) = \overrightarrow a × \overrightarrow b + \overrightarrow a × \overrightarrow c$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If either $ \overrightarrow a = \overrightarrow 0 $ or $ \overrightarrow b = \overrightarrow 0 $ then $ \overrightarrow a × \overrightarrow b = \overrightarrow 0$. Is the converse true? Justify your answer with an example.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the area of the triangle with vertices $A(1, 1, 2), B(2, 3, 5)$ and $C(1, 5, 5)$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Area of a rectangle having vertices $A, B, C$ and $D$ with position vectors $ -\hat i + \large\frac{1}{2}$$ \hat j + 4\hat k, \: \hat i +\large \frac{1}{2}$$ \hat j + 4\hat k, \: \hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ and $-\hat i -\large \frac{1}{2}$$ \hat j + 4\hat k$ respectively is

asked Dec 5, 2012 by thanvigandhi_1

1 answer

A girl walks 4 km towards west, then she walks 3 km in a direction 30° east of north and stops. Determine the girl’s displacement from her initial point of departure.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Show that the points A(1, – 2, – 8), B (5, 0, – 2) and C (11, 3, 7) are collinear, and find the ratio in which B divides AC.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are $(2\overrightarrow a + \overrightarrow b)$ and $(\overrightarrow a - 3\overrightarrow b)$ externally in the ratio 1 : 2. Also, show that P is the mid point of the line segment RQ

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The two adjacent sides of a parallelogram are $2\hat i - 4\hat j + 5\hat k$ and $ \hat i - 2\hat j - 3\hat k$ . Find the unit vector parallel to its diagonal. Also, find its area.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Let $\overrightarrow a = \hat i + 4 \hat j + 2\hat k, \overrightarrow b = 3\hat i − 2 \hat j + 7\hat k \: and \: \overrightarrow c = 2\hat i − \hat j + 4\hat k $ . Find a vector $ \overrightarrow d$ which is perpendicular to both $\overrightarrow a$ and $\overrightarrow b$ , and $ \overrightarrow c ⋅ \overrightarrow d =15$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

The scalar product of the vector $\hat i + \hat j + \hat k$ with a unit vector along the sum of vectors $2\hat i + 4 \hat j − 5\hat k$ and $λ\hat i + 2 \hat j + 3\hat k$ is equal to one. Find the value of $ λ.$

asked Dec 5, 2012 by thanvigandhi_1

1 answer

If $ \overrightarrow a, \overrightarrow b, \overrightarrow c, $ are mutually perpendicular vectors of equal magnitudes, show that the vector $ \overrightarrow a + \overrightarrow b + \overrightarrow c$ is equally inclined to $ \overrightarrow a, \overrightarrow b and \overrightarrow c$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Prove that $ (\overrightarrow a + \overrightarrow b) ⋅ (\overrightarrow a + \overrightarrow b) =| \overrightarrow a |^2 + |\overrightarrow b |^2$, if and only if $\overrightarrow a,\: \overrightarrow b$ are perpendicular, given $\overrightarrow a ≠ 0, \overrightarrow b ≠ 0$.

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Choose the correct answer in the following : let $ \overrightarrow a$ and $ \overrightarrow b$ be two unit vectors and θ is the angle between them. Then $ \overrightarrow a\ + \overrightarrow b$ is a unit vector if

asked Dec 5, 2012 by thanvigandhi_1

1 answer

Integrate the rational functions $\frac{(x^2+1)(x^2+2)}{(x^2+3)(x^2+4)}$

asked Dec 4, 2012 by sreemathi.v

1 answer

Integrate the rational functions $\frac{1}{(e^x-1)} [Hint:Put\;e^x=\;t]$

asked Dec 4, 2012 by sreemathi.v

1 answer

Choose the correct answer in $\Large \int \normalsize\frac{\large xdx}{\large (x-1)(x-2)}$ equals\begin{array}{1 1}(A)\;log\mid\frac{(x-1)^2}{x-2}\mid+\: C & (B)\;log\mid\frac{(x-2)^2}{x-1}\mid+\: C\\(C)\;log\mid\bigg(\frac{x-1}{x-2}\bigg)^2\mid+\: C & (D)\;log\mid(x-1)(x-2)\mid+ \: C\end{array}

asked Dec 4, 2012 by sreemathi.v

1 answer

Using the fact that $\sin (A + B) = \sin A \cos B + \cos A \sin B$ and the differentiation, obtain the sum formula for cosines.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

Using mathematical induction prove that $ \large\frac{d}{dx}\normalsize (x^{\large n}) = nx^{\large{n-1}} $ for all positive integers $n$.

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If $x = a (\cos t + t\sin t)$ and $y = a (\sin t - t \cos\: t)$, find $ \large\frac{d^2y}{dx^2}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

If $cos\: y = x \cos (a + y)$, with $\cos$ $a \neq \pm 1$, prove that $ \large\frac{dy}{dx}=\frac{\cos^2(a + y)}{\sin \: a}$

asked Dec 4, 2012 by thanvigandhi_1

1 answer

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